Functional analysis, stochastic analysis and applications

In general, the investigations will include functional and stochastical analysis, concerning also their frequent applications. More precise, we investigate: linear bounded and unbounded operators on Banach and Hilbert spaces, Banach and C*algebras, Hilbert C* modules, Fredholm and spectral properties, complex matrices, matrix equations and inequalities, solving various equations numerically, generalized invertibility in rings, different concepts of summability, classes of transformations on sequence spaces, infinite matrices, stochastic differential equations, stochastic integral equations, existence and stability of SDE and SIE, solving these equations analytically and numerically, define and investigate new distributions, estimation of parameters and forecast time series, time series with outliers, numerical simulations of defined time series, the asymptotic analysis of second-order nonlinear ordinary and functional differential equations in the framework of regularly varying functions, define and investigate new classes of generalizations of orthogonal polynomials, implementation of obtained results in economy, ecology, epidemiology, physics, mechanics, as well as in other relevant sciences and social aspects.